If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?
Practice Questions
1 question
Q1
If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?
G * M * m / (R + h)^2
G * M * m / R^2
G * M * m / (R - h)^2
G * M * m / (R + h)
The gravitational force acting on the satellite is given by Newton's law of gravitation, which states that F = G * (M * m) / (R + h)^2, where M is the mass of the Earth and m is the mass of the satellite.
Questions & Step-by-step Solutions
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Q
Q: If the radius of the Earth is R and a satellite is in a low Earth orbit at a height h, what is the expression for the gravitational force acting on the satellite?
Solution: The gravitational force acting on the satellite is given by Newton's law of gravitation, which states that F = G * (M * m) / (R + h)^2, where M is the mass of the Earth and m is the mass of the satellite.
Steps: 5
Step 1: Understand that the gravitational force between two objects is described by Newton's law of gravitation.
Step 2: Recall the formula for gravitational force: F = G * (M * m) / d^2, where F is the gravitational force, G is the gravitational constant, M is the mass of the larger object (Earth), m is the mass of the smaller object (satellite), and d is the distance between the centers of the two objects.
Step 3: Identify the distance d. The distance from the center of the Earth to the satellite is the radius of the Earth (R) plus the height of the satellite (h). So, d = R + h.
Step 4: Substitute d into the gravitational force formula. This gives us F = G * (M * m) / (R + h)^2.
Step 5: Conclude that the expression for the gravitational force acting on the satellite is F = G * (M * m) / (R + h)^2.
